We use data on insurance deductible choices to estimate a structural model of risky choice that incorporates standard risk aversion (diminishing marginal utility for wealth) and probability distortions. We find that probability distortions - characterized by substantial overweighting of small probabilities and only mild insensitivity to probability changes - play an important role in explaining the aversion to risk manifested in deductible choices. This finding is robust to allowing for observed and unobserved heterogeneity in preferences. We demonstrate that neither Kõszegi-Rabin loss aversion alone nor Gul disappointment aversion alone can explain our estimated probability distortions, signifying a key role for probability weighting.